BS1363 is not the only type with shutters or insulated pins these days. Although, insulated pins are not so important where the plug mating face engages in a deep pocket in the socket front, such as CEE7/3 Schuko.
BS1363 is a good plug that benefits from being of more recent design than most, engineered to meet a specification based on experience of other good plugs including BS372 and derivatives. But the fuse is an Achilles heel due to its heat dissipation and its requirement for fuse contacts of excellent design and manufacture. If these are in any way lacking in quality, and many are (compared to say the original MK Safety Plug) they are markedly unreliable on high load and prone to thermal runaway. This is not a fault with the design as such, but nonetheless it gives rise to a range of common failure modes that would not exist if there were no fuse.
In contrast, a moulded unfused plug with spot-welded leads has no pressure contacts internally and unless of genuinely faulty manufacture cannot exhibit significant resistance or generate significant heat even under overload. Only the socket and switch contacts dissipate significant heat, and if you have spent much time dissecting and testing typical sockets from around the world, you will know that run-of-the-mill BS1363 socket contacts are not always the lowest-resistance offering out there. A well-made Schuko socket will handle 20A continuously, giving a useful safety margin to avoid thermal runaway at 16A.
No one design currently in use has all the best features. Some have very few of them. Some locales tend not to use plugs at all, preferring to push wires into sockets. Shutters are a real nuisance here and well worth avoiding.